What is the limit as x approaches 0+of (1-4x)^{1/x} ?

The limit as x approaches 0+of (1-4x)^{1/x} is 1/(e^4)

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limit as x approaches 0+of (1-4x)^{1/x}

x \to 0 + lim ((1 - 4 x)^{\frac{1}{x}})

\frac{1}{e ^{4}}

Decimal Notation

0.01831 \dots

Solution steps

x \to 0 + lim ((1 - 4 x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{1}{x} l n (1 - 4 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{4}}

= \frac{1}{e ^{4}}

\int 6 x (3 x^{2} + 4)^{4} d x

\frac{d}{d x} (\frac{( x - 2 ) ^{3}}{x ^{2}})

\frac{\partial}{\partial x} (x^{3} + y^{3} - 3 x y)

f (x) = 7 e^{x} cos (x), at x = 0

What is the limit as x approaches 0+of (1-4x)^{1/x} ?
The limit as x approaches 0+of (1-4x)^{1/x} is 1/(e^4)